While every game has its own variation on the of a Rogue, they pretty much always center around the same core concept: stealth & evasion. In almost every game with such a class, the Rogue is usually able to go invisible for either a limited or unlimited period of time, and their chances of remaining undetected usually depends on their skill level. Simply put, the more points a player puts into the stealth (or equivelant there-of) skill, the less chance of being detected. For the most part, they also have a natural affinity for traps, both in setting them and disarming them.
Not every game sticks with this principle, but generally speaking Rogues are a class that's limited to using simple or short weapons such as daggers. World of Warcarft, for instance, doesn't really abide by this rule and allows Rogues to use swords as well. This does, however, comes with limitations, such as not being able to use certain stealth skills, requiring them instead to use a dagger for those.
For a large part, Rogues are considered to be high DPS classes, and they are often used as strong offensive characters. This usually comes at the cost of having a mediocre defense, which means they aren't useful for Tanking. However, because of their high damage rating, sneak attacks, and their ability to become invisible, they are often formidable foes who can quickly incapacitate and ultimately kill their adversaries.
In EverQuest, rogues are the masters of stealth and weaponry. They truly shine when in a group of adventurers where the enemy is focused on others, which allows the rogue to prove himself/herself as the best damage dealing melee class thanks to their Backstab ability. Rogues can also work as scouts for their allies using the sneak/hide ability that allows them to traverse unseen by most enemies. This also allows Rogues to retrieve fallen friends' bodies from the clutches of enemy camps. In many dungeons, there are locked doors that can be picked by having an adept rogue in your group. Rogues are relegated to leather or chain armor and cannot solo very well considering most of their damage is dealt from behind an enemy. Rogues also have the unique skill of Poisoncrafting, which allows them to increase the already lethal damage of their blades with the application of status affecting poisons. They can also pick the pockets of most enemies, taking money and valuable gems before the rest of the group knows what loot the enemy carried.
While not an RPG franchise, Assassin's Creed is still a stealth-driven game that have players control cloaked rogues, exploring open-worlds to sneak past enemies and perform feats of agility, such as climbing up, running above, and jumping buildings.